Question

A standing wave is set on a string of length $3\text{m}$ which is fixed between two points. If the number of loops formed is four, then calculate the frequency of wave. Given velocity of wave is $18{\text{ms}}^{-1}$.

• A. $12\text{Hz}$
• B. $6\text{Hz}$
• C. $18\text{Hz}$
• D. $24\text{Hz}$

Answer 1

The correct option is A $12\text{Hz}$


According to the question, there are $4$ loops in $3\text{m}$.

$\Rightarrow 4\times \frac{\lambda }{2}=3$

$\therefore \lambda =\left(\frac{3}{2}\right)\text{m}$

Given that, the velocity of the wave,

$V_m=18{\text{ms}}^{-1}$

Frequency,

$f=\left(\frac{V_m}{\lambda }\right)=\frac{18}{\left(\frac{3}{2}\right)}=12\text{Hz}$

Hence, option $\left(A\right)$ is correct.